Particles floating at an interface, in general, self-assemble or cluster because they deform the interface, thus giving rise to lateral capillary forces which cause the particles to cluster. For example, cereal flakes floating on the surface of milk cluster by this mechanism. The attractive lateral capillary forces arise due to the fact that for two floating particles, the deformed interface is such that the interface height between the particles is lowered due to the interfacial tension. See, for example, M. A. Fortes, “Attraction and repulsion of floating particles”, Can. J. Chem. 60, 2889 (1982); W. A. Gifford and L. E. Striven, “On the attraction of floating particles”, Chem. Engrg. Sci. 26, 287-297 (1971); Kralchevsky, P. A., V. N. Paunov, N. D. Denkov, I. B. Ivanov and K. Nagayama. “Energetical and force approaches to the capillary interactions between particles attached to a liquid-fluid interface”, J. Colloid and Interface Sci. 155, 420-437 (1993), J. Lucassen, “Capillary forces between solid particles in fluid interfaces”, Colloids Surf. 65, 131-137 (1992); and P. Singh and D. D. Joseph, “Fluid dynamics of Floating particles”, J. Fluid Mech. 530, 31-80 (2005). The lateral component of the capillary force acting on the particles is attractive and causes them to move towards each other.
This naturally occurring phenomenon, however, produces monolayers that display many defects, lack order (both short and long ranged) and whose distance between the particles cannot be controlled. These are three drawbacks which seriously limit the range of applications one can target using this technique. In addition, such a phenomenon does not manifest itself on particles smaller than ˜10 μm, which further limits the applications for this technique.
The vertical position of a floating particle within a two-fluid interface is such that the total force acting on it in the direction normal to the interface is zero, and this position determines the extent of interfacial deformation and lateral capillary forces. A particle that is denser than the liquid below can float on its surface because the vertical component of capillary force, which arises due to the deformation of the interface, balances the particle's buoyant weight.
As mentioned above, such a phenomenon does not manifest itself on particles smaller than ˜10 μm. In particular, for a small particle of radius a, the buoyant weight, which scales as a3, becomes negligible compared to the capillary force, which scales as a, and therefore insignificant interfacial deformation is needed for balancing the buoyant weight of small particles. Consequently, the lateral capillary forces due to the deformation of the interface are too small to move micron and submicron sized particles, and thus, small particles, in general, do not self-assemble under the action of capillary forces alone. However, small particles can self-assemble if they are charged or if they have irregular contact lines.
Many envisioned applications of nanotechnology and fabrication of mesoscopic objects strongly rely on the manufacturing of such micro- and nano-structured materials. Future progress in this area will critically depend upon our ability to accurately control the particles arrangement (e.g., lattice spacing, defect-free capability and long range order) in three dimensions (3D) as well as in two dimensions (2D) for a broad range of particle sizes, shapes, and types.
Accordingly, there is a need for improved methods and systems for the fabrication of self-assembled, defect-free adjustable monolayers of particles. Those and other advantages of the present invention will be described in more detail hereinbelow.